Can we calculate mean recall and precision
For the precision metric for example you have:

$$
 Precision = \frac{TP}{TP+FP},
$$
with TP = True Positive and FP = False Positive.

Imagine you have the following values:
Image 1: $TP = 2, FP = 3$
Image 2: $TP = 1, FP = 4$
Image 3: $TP = 3, FP = 0$  

The precision scores as you calculated will be:
Image 1: $2/5$
Image 2: $1/5$
Image 3: $1$
Your average will be: $0.533$

On the other hand if you sum them all up and then calculate the precision value you get:

$P = \frac{6}{6+7} = 0.462$

This proves that averaging the precision scores is not the same as calculating the total precision in one go.

Since what you want is to know how precise your algorithm is, independently of the precision for each image, you should sum all the TP and FP and only then calculate the precision for each model. This way you will not have a biased average. The average would give the same weight to an image with a larger number of objects as to another image which had fewer objects.